This passage makes the connection between the first part of the letter, which speaks of the condemnation of humanity because of the sin of Adam and the justification through Christ, and the three chapters that deal with the sanctification and the sin in human nature.
To understand this text properly, you need to take into account that there are three types, or aspects, of death:
From what was exposed in the previous chapters, we conclude that sin entered the world by Adam and as a result, death passed to his descendants, which form the whole of humanity, because all sinned. "Sin" is personified as if it were something pre-existing already and brought into the world of humanity, and "death" is both physical and spiritual, a remoteness from God.
Nothing more is said about the origin of evil, and in the period between the sin of Adam until the delivery of the law through Moses, God had not subjected anybody to a law written by Him. Without law, it is clear that there could be no trespass of a law, and there being no trespass, there could not be a sin of transgression of the law, thus explaining the sentence "sin (transgression) is not imputed when there is no law ".
Even without the written law, however, everyone in his conscience had the knowledge of good and evil, and God still spoke with Adam and a few other people, giving instructions that were passed on to their generations.
For about twenty-four centuries after the creation of Adam, the world's population had multiplied and those who were born had very long lives, of several centuries (Genesis 5). There was polygamy, and eventually "… the LORD saw that the wickedness of man was great in the earth, and that every intent of the thoughts of his heart was only evil continually” (Genesis 6: 5). God then killed all humans with a worldwide flood, with the exception of Noah and his family.
Thus, "death reigned" during all this time, that is, humanity died physically and spiritually because it did not have communion with God, proving that sin is not limited to the transgression of a pact with God (as the law of Moses) or a specific prohibition (made to ADAM).
However there was the exception of those who began to call upon the name of the Lord from the time of Seth (Genesis 4:26), of which we have the examples of Enoch and Noah (Genesis 5:24 and Genesis 6:8). Enoch seems to have passed by physical death because "he was not, for God took him.”
God-fearing Noah gave rise to a new humanity that, unfortunately, soon turned to impiety. The law was given to the people of Israel ten centuries later.
Although the sacrificial death of Christ is offered as a propitiation for the sins of humanity, only those who accept it ("many" in the text) enjoy all of its benefit. Christ represented and gives rise to all those who are justified (the new creation), just like Adam represented and gave rise to all sinners (the old creation).
It is in this sense that Adam “is a type of Him who was to come" (v. 14). The Bible teaches that all humankind is sinful, both in its nature as by practice. All have human parents, inherit the sin of the parents and add their own choice.
Spiritual death, which is eternal separation from God, is the immediate consequence of sin. Having died, we must be "born again" to re-establish communion with God and nobody is able to do this for himself. As descendants of Adam, we are all subject to judgment and condemnation because we are sinners by nature, we have inherited the sin of Adam, and we practise sin.
However, God even paved the way not only for the restoration of this communion, but to make it effective for all eternity, granting the sinner "eternal life". To be able to satisfy his righteousness, God sent His Son into the world to give His life on the cross as a substitute for sinners.
Salvation from sin and its penalty is offered freely to all humankind through faith in the Lord Jesus Christ. Those who reject salvation by faith in Christ add it to their sins, and rejection is the biggest sin of all, for which there is no pardon (John 3:18 -19 and 3:36).
As for those who have never heard the Gospel of Christ, God, who is a righteous judge, will judge their situation. All His decisions are just and are made with the greatest equity. What seems to be a problem in our weak and flawed sight, is not a problem for him, and nobody will have a legitimate basis to oppose His decision.
Christ's death was unique because His death was not a consequence of Adam's sin, as in the case of the rest of humanity. Being perfect in his humanity, sinless, he was not subject to death. He gave his life voluntarily, and when he physically died his spirit went to Sheol, the place of the dead, the part intended for the righteous called Paradise, which the Jews called "bosom of Abraham" (Psalm 16:10, Lucas 23:43, Acts 2:27, 31).
He was able, therefore, to give His life voluntarily as the price for the remission of sin of men, having taken upon himself the punishment that we should pay, of which the lamb of the sacrifices of the law of Moses were a symbol. God, who gave us proof by raising Him from the dead after three days, accepted the price He paid.
After resurrecting, Jesus Christ ascended to the presence of God taking with Him Paradise and its inhabitants (Ephesians 4:8). He is sufficient for a much more abundant justification than just the condemnation for the sin of Adam, because:
This way, the problem of the entrance of sin in the world was resolved and it can be argued that the solution brought even more blessings to the man who converts to Christ than he would have in the initial state of innocence.
Now he is a son of God, heir of God or coheir with Jesus Christ. He has the promise of a home in heaven and to be with Christ, of being as He is, forever. All because of the redemptive work of Jesus Christ, our Lord.
12 Therefore, just as through one man sin entered the world, and death through sin, and thus death spread to all men, because all sinned—
13 (For until the law sin was in the world, but sin is not imputed when there is no law.
14 Nevertheless death reigned from Adam to Moses, even over those who had not sinned according to the likeness of the transgression of Adam, who is a type of Him who was to come.
15 But the free gift is not like the offense. For if by the one man's offense many died, much more the grace of God and the gift by the grace of the one Man, Jesus Christ, abounded to many.
16 And the gift is not like that which came through the one who sinned. For the judgment which came from one offense resulted in condemnation, but the free gift which came from many offenses resulted in justification.
17 For if by the one man's offense death reigned through the one, much more those who receive abundance of grace and of the gift of righteousness will reign in life through the One, Jesus Christ.)
18 Therefore, as through one man's offense judgment came to all men, resulting in condemnation, even so through one Man's righteous act the free gift came to all men, resulting in justification of life.
19 For as by one man's disobedience many were made sinners, so also by one Man's obedience many will be made righteous.
20 Moreover the law entered that the offense might abound. But where sin abounded, grace abounded much more,
21 so that as sin reigned in death, even so grace might reign through righteousness to eternal life through Jesus Christ our Lord.